Title:On the Light Massive Flavor Dependence of the Top Quark Mass

Abstract: We provide a systematic renormalization group formalism to study the mass
effects in the relation of the pole mass and short-distance masses such as the
$\overline{\mathrm{MS}}$ mass of a heavy quark $Q$, coming from virtual loop
insertions of massive quarks lighter than $Q$ with the main focus on the top
quark. The formalism reflects the constraints from heavy quark symmetry and
entails a combined matching and evolution procedure that allows to disentangle
and successively integrate out the corrections coming from the lighter massive
quarks and the momentum regions between them and also to precisely control the
large order asymptotic behavior. The formalism is used to study the asymptotic
behavior of light massive flavor contributions and is applied to predict the
${\cal O}(\alpha_s^4)$ virtual quark mass corrections, calculate the pole mass
differences for massive quark flavors with a precision of around 20 MeV, and
determine the pole mass ambiguity which amounts to 250 MeV in the physical case
of three massless quark flavors.